What is Place Value?
Our number system contains the digits 0 through 9.
How do we represent a number greater than 9? We start by counting groups. In our number system we count groups of ten.
Here are 3 groups of ten:
We write numbers by placing digits side by side. The value of each digit is determined by its place. Here the three in the tens place represents three groups of ten. What if we having nothing in a place? We use zero.
Since our number system is based on ten we call it a base ten number system. Each place in a number has a value that is ten times the value of the position immediately to the right.
It can be helpful to show the value of each digit in a number by writing it in expanded form (also called decomposing):
Why is it important?
We need to understand how to move value from one place to another (regrouping, carrying, borrowing) to do multi-digit number arithmetic. Without a grasp of the value of every digit in a number these operations can be difficult to understand.
Use playing cards to make the highest number possible. Only work with the number cards from a deck, not the king, queen or jack. The ace can be used as one. Flip over three cards. Look at the numbers on each card. Arrange the cards to make the highest number possible. Keep score by writing out each number in standard and expanded form.